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musickatia [10]
3 years ago
5

Find the annual percent increase or decrease that y = 0.35(2.3)x models. (1 point) A.230% increase B.130% increase C.30% decreas

e D.65% decrease
Mathematics
2 answers:
ipn [44]3 years ago
8 0

Answer: B. 130% increase


Step-by-step explanation:

Given function :  y=0.35(2.3)^x

If x represents the number of years, we have to determine the two values of y in consecutive terms to determine if the value of y increases or decreases after a year.


This function is equivalent to the exponential growth function


y=A(1+r)^x, where A=0.35 and (1+r)=2.3, [A= initial amount , r=annual percent increase]

Thus,

\Rightarrow\ r=2.3-1\\\Rightarrow\ r=1.3\\\Rightarrow\ r=1.3\times100\%=130\%

Hence, the annual percent increase is 130%.

rosijanka [135]3 years ago
7 0

The annual percent of the model y = 0.35{\left( {2.3}\right)^x} is increases by \boxed{130\% }. Option (B) is correct.

Further explanation:

The exponential growth function or compound interest formula can be expressed as follows,

\boxed{A = C{{\left( {1 + i} \right)}^x}}

Here, A represents the total amount, C represents the initial amount, irepresent the annual percentage increase and x represents the time.

Given:

The annual percentage model can be expressed as,

y = 0.35{\left( {2.3} \right)^x}

The options of annual percentage are given as follows.

A. 230\% {\text{ increases}}.

B. 130\% {\text{ increases}}.

C. 30\% {\text{ decreases}}.

D. 65\% {\text{ decreases}}.

Explanation:

Compare given model y = 0.35{\left( {2.3} \right)^x} with the exponent growth model y = 0.35{\left( {2.3}\right)^x}.

The value of C is 0.35 and the value of \left( {1 + i} \right) is 2.3.

\begin{aligned}1 + i&= 2.3\\i &=2.3 - 1\\i &= 1.3\\\end{aligned}

The function is increases by 130\%.

Option A is not correct.

Option B is correct.

Option C is not correct.

Option D is not correct.

Hence, the annual percent of the model y = 0.35{\left( {2.3}\right)^x} is increases by \boxed{130\% }. Option (B) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment

Keywords: Annual percentage, increases or decreases, model, interest rate, simple interest, compound interest, annual payment, annuity.

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Determine how long it will take for a principal amount of $13,000 to double its initial value when deposited into an account pay
bezimeni [28]

Compound interest can be defined as the interest <em>on a deposited amount, an investment</em> that is <em>compounded based on its principal and interest rate.</em>

It will take about 3.239 years for the principal amount of $13,000 to double its initial value.

From the above question, we can deduce that we are to find the time "t"

The formula to find the time "t" in compound interest is given as:

t = ln(A/P) / r

where:

P = Principal = $13,000

R = Interest rate = 21.4%

A = Accumulated or final amount

From the question, the Amount "A" is said to be the double of the principla.

Hence,

A = $13,000 x 2

= $26,000

  • Step 1: First, convert R as a percent to r as a decimal

r = R/100

r = 21.4/100

r = 0.214 per year.

  • Step 2: Solve the equation for t

t = ln(A/P) / r

t = ln(26,000.00/13,000.00) / 0.214

t = 3.239 years

Therefore, it will take about 3.239 years for the principal amount of $13,000 to double its initial value.

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